Question

simplify 3/x+13/x−11

and explain please !

Answer 1

the problem is

\[\large \frac{3}{x} + \frac{13}{x-1}\]

right?

Answer 2

no, its an 11 not a 1 @jim_thompson5910

Answer 3

oh so

\[\large \frac{3}{x} + \frac{13}{x-11}\]

sry misread

Answer 4

yessir @jim_thompson5910

Answer 5

ok

Answer 6

The idea is to get each fraction to have the same denominator (the LCD).


In this case, the LCD is x(x-11)


To get the first fraction have a denominator of x(x-11), you need to multiply top and bottom by (x-11), which is the missing piece here.


To get the second fraction have a denominator of x(x-11), you need to multiply top and bottom by x, which is the missing piece here.


Afterwards, you can combine the numerators over the common denominator.


\[\large \frac{3}{x} + \frac{13}{x-11}\]


\[\large \frac{3(x-11)}{x(x-11)} + \frac{13}{x-11}\]


\[\large \frac{3x-33}{x(x-11)} + \frac{13}{x-11}\]


\[\large \frac{3x-33}{x(x-11)} + \frac{x*13}{x(x-11)}\]


\[\large \frac{3x-33}{x(x-11)} + \frac{13x}{x(x-11)}\]


\[\large \frac{3x-33+13x}{x(x-11)}\]


\[\large \frac{16x-33}{x(x-11)}\]


\[\large \frac{16x-33}{x^2 - 11x}\]


Note: the last step is (usually) optional

Answer 7

so "x-11' is the LCD @jim_thompson5910